The Art of Quantitative Finance Vol. 3: Risk, Optimal Portfolios, and Case Studies

Preface to Volume III
About This Book
Contents
1 Risk Measurement and Credit Risk Management
1.1 Simple Risk Measures and Basic Features of CreditRisk Management
1.2 Value at Risk
1.3 Calculating VaR for Simple Portfolio Examples: Example 1 (an Index)
1.4 Excursus: Distribution of the Minimum of a Brownian Motion and Calculation of the Adapted VaR
1.5 Calculating VaR for Simple Portfolio Examples: Example 2 (a Stock Index in Foreign Currency) and Stress Testing
1.6 Example 3: VaR of a Portfolio of Two Stocks as a Function of Their Correlation
1.7 Example 4: VaR Estimation for a Simple Options Strategy
1.8 Conditional VaR
1.9 CVaR Estimation: Some Examples
1.10 Credit Risk Management: Introduction
1.11 Credit Metrics, Part I: Basic Approach
1.12 Credit Metrics, Part II: Ratings and Fair Value of Bonds at Risk of Default
1.13 Credit Metrics, Part III: Rating Transition Probabilities and Expected Value of the Loan Portfolio in 1 Year
1.14 Credit Metrics, Part IV: Variance of a Credit Portfolio's Value in 1 Year
1.15 Credit Metrics, Part V: Variance of a Credit Portfolio's Value in 1 Year
1.16 Credit Metrics, Part VI: The Asset Value Model for Determining Joint Credit Rating Transition Probabilities
1.17 Credit Metrics, Part VII: Determining the Percentile of A1 Using Monte Carlo Simulation
1.18 Credit Metrics, Part VIII: Detailed Example with Variants
1.19 Excursus: Generating Positive Definite RandomCorrelation Matrices
1.20 Credit Risk+, Part I: Basic Concept and Expected Number of Defaults Assuming Independent Loans
1.21 Credit Risk+, Part II: Expected Loss Amount Assuming Independent Loans
1.22 Credit Risk+, Part III: Allocating Loans to Mutually Independent Sectors
1.23 Credit Risk+, Part IV: Allocation of Loans to Mutually Independent Sectors and Determination of RequiredCapital Ratio
1.24 Credit Risk+, Part V: An Illustrative Example
References
2 Optimal Investment Problems
2.1 Classic Portfolio Optimization According to Markowitz, Part 1: Fundamental Principles
2.2 Classic Portfolio Optimization According to Markowitz, Part 2: Two Financial Assets
2.3 Classic Portfolio Optimization According to Markowitz, Part 3: Two Assets, Efficient Border
2.4 Classic Portfolio Optimization According to Markowitz, Part 4: Two Assets, with Short Selling
2.5 Classic Portfolio Optimization According to Markowitz, Part 5: Two Risky Assets and One Risk-Free Asset. Portfolios with Maximal Sharpe Ratio
2.6 Classic Portfolio Optimization According to Markowitz, Part 6: Two Risky Assets and One Risk-Free Asset:Practical Example
2.7 Classic Portfolio Optimization According to Markowitz, Part 7: Sketch of a Sensitivity Test
2.8 Classic Portfolio Optimization According to Markowitz, Part 8: Arbitrary Number of Assets, Principal Form ofOpportunity Sets
2.9 Classic Portfolio Optimization According to Markowitz, Part 9: Arbitrary Number of Assets, Explicit Calculation of Efficient Border, and Portfolio with Maximal Sharpe Ratio: Planning the Procedure
2.10 Classic Portfolio Optimization According to Markowitz, Part 10: Arbitrary Number of Assets, Explicit Calculation of Efficient Border, and Portfolio with Maximal Sharpe Ratio
2.11 Classic Portfolio Optimization According to Markowitz, Part 11: Arbitrary Number of Assets, Explicit Calculation of Efficient Border, and Portfolio with Maximal Sharpe Ratio: Practical Example
2.12 The ``Market Portfolio'': The Portfolio with MaximalSharpe Ratio
2.13 Portfolio Selection Based on a Single-Index Model
2.14 The Optimal Investment and Consumption Problem: Introduction and Formulation of the Problem
2.15 Fundamentals of Stochastic Control Theory, the HJB Equations
2.16 An Application Example for the HJB Equation: The Linear Regulator
2.17 Solving the Optimal Consumption Investment Problem
References
3 Case Studies
3.1 Case Study I: The Fynup Ratio
3.1.1 The Task
3.1.2 Definition of Terms and General Remarks
3.1.3 Technical Preparations
3.1.4 One Possible Intuitive Approach
3.1.5 The Principle of the Fynup-Ratio Approach: Determination of Weights – Schematic
3.1.6 The Principle of the Fynup-Ratio Approach: Determination of Weights – Technical Details
3.1.7 Optimization Using a Monte Carlo Method
3.1.8 Adaptation of Weight Selections
3.1.9 Indication for Funds with at Least 10 Years of History
3.1.10 Informal Indication for Funds with Less Than 10 Years of History
3.1.11 The Result and the Percentile Representation
3.1.12 Informative Value of the IndicationResults – Conclusions
3.2 Case Study II: Expert Witness Opinion on Churning
3.2.1 Specifics of the Case
3.2.2 The Question in a More Precise Wording
3.2.3 Modelling the Underlying Assets
3.2.4 Profit Probabilities for the Individual Positions When Held to Expiration
3.2.5 Profit Probabilities for the Individual Positions in the Case of Profit-Taking Before Expiration
3.2.6 Profit-Taking Probabilities for the Option Portfolio
3.3 Case Study III: Pricing an Interest Rate Swap and Analysing Its Suitability for Optimizing a Loan Portfolio
3.3.1 Presentation of the Case, the Products, and the Issues
3.3.2 Fair Value of the Swap at Inception: Part 1 – Interest Rate Swap Component
3.3.3 Fair Value of the Swap at Inception: Part 2 – Option Component
3.3.4 Regarding the Intent of Achieving ``Portfolio Optimization'' by Using the Swap
3.4 Case Study IV: Valuation of Callable Range Accrual Swaps as Part of an Expert Opinion
3.4.1 The Product
3.4.2 Motivation for Entering into the Swap and Further Background Information
3.4.3 Modelling and Calibration of the Requisite Interest Rates in the Vasicek Model
3.4.4 Valuation of the RAS Based on the Vasicek Model without Considering the Termination Right
3.4.5 Valuation of the RAS Based on the Vasicek Model with Termination Right
3.4.6 Test of the Risk-Free Model's Calibration Quality and Sensitivity Analysis of the Results
3.5 Case Study V: Analysis of the Performanceof Put-Write Strategies
3.5.1 Setup of the Tested Put-Write Strategies
3.5.2 Discussion and Examples of Some Parameter Choices
3.5.3 The Various Parameter Choices and Selection of Some Analysis Results
3.5.4 Variant: 2-M Strategy
3.5.5 Instructions for the Use of the Analysis Program on the Website
3.5.6 Closing Remarks on Operational Risks and Strategy Variants
3.6 Case Study VI: Valuation of an Asian Option on the Basis of a Foreign Currency Loan Within the Scope of an Expert Witness Report
3.6.1 Overall Product Structure
3.6.2 Fair Price of the Guarantee Bond in Asian and European Style
3.6.3 Preparation of an Ex Ante Risk Assessment from the Perspective of Realistic Earnings Prospects When Using Debt Financing
3.6.4 Actual Performance of the Product Combination
3.7 Case Study VII: Expert Opinion on the EUR CHF Stop-Loss Order Fiasco in January 2015
3.7.1 Analysis of Comparable Events: GBP DEM September 1992
3.7.2 The GBP DEM Case: Comparison of Stop Loss Versus Hedging with Put Options in the Period October 1990 to October 1992
3.7.3 The GBP DEM Case: Hedging with Put Options for 10-Year Loans as from October 1990
3.7.4 Alternative Hedging Method for the EUR CHF Exchange Rate Using Put Options
3.7.5 Hedging Using Put Options for 10-Year or 20-Year Loans as from January 2012
3.7.6 Comparison with the Stop-Loss Approach
3.8 Case Example VIII: Analyses of the Risk of Individual Higher-Quality Bonds Versus Portfoliosof Lower-Quality Bonds
3.8.1 Two Simple Hypothetical Examples for Illustration
3.8.2 Analyses Based on Realistic Data
3.9 Case Study IX: Portfolio Selection Based on Sustainability Parameters
3.9.1 The Problem
3.9.2 Monte Carlo Determination of Efficient Frontiers and Market Portfolios Subject to Sustainability Constraints and Optimal Sustainability Sharpe Parameters in the Case without Short Selling
3.9.3 Determination of Efficient Frontiers and Market Portfolios Subject to Sustainability Constraints and Optimal Sustainability Sharpe Parameters in the Case with Short Selling
3.9.4 Outlook
3.10 Case Study X: Comparison of Two Basket Derivatives
3.10.1 Detailed Description of the Two Products
3.10.2 First Brief Comparison of the Two Products
3.10.3 Comparison of the Two Product Values on 1 June 2008
3.11 Case Study XI: Optimal Hedging with Future Contracts in Connection with Liquidity Risks and the ``Metallgesellschaft''Case
3.11.1 Presentation of the Hedging Strategy and the Problem
3.11.2 Translation of the Problem into the Continuous Case and Glasserman's Strategies
3.11.3 The Solution to the Optimal Hedging Problem
3.11.4 The Proof Sketch
3.12 Case Study XII: Computing the Payout Ratios for a Financial Market Game
3.12.1 Description of the Game
3.12.2 Computation of the Payout Ratio
3.12.3 Computation of Probability P1
3.12.4 Computation of Probabilities P2 and P3
3.12.5 Testing the Results Using Monte Carlo Simulation and Concluding Remarks
3.13 Case Study XIII: Trading Strategies Based on Hedging
3.13.1 Background
3.13.2 An Initial Idea of a Trading Strategy
3.13.2.1 The Strategy
3.13.2.2 Implementation in Reality
3.13.2.3 Estimating Realized Volatility
3.13.2.4 Executing the Strategy on an Example
3.13.2.5 Analysing the Strategy Through Backtesting
3.13.2.6 Extension of the Strategy
3.13.3 A Second Variant of the Strategy
3.13.3.1 Analysing the Strategy Through Backtesting
3.14 Case Study XIV: Analysis of the Derivative Trading Strategy ``Lambda +''
3.14.1 Introduction
3.14.2 Definition of the Strategy and Its Variants
3.14.3 The Task and the Analyses
References